论文标题
在排队系统中,最佳和自我选择的服务类型,长期服务推迟了对下一个服务的需求
Optimal and Self Selection of Service Type in a Queueing System where Long Service Postpones the Need for the Next Service
论文作者
论文摘要
我们研究了一个有限客户的订购系统。生产是随机的,有序数量和生产率之间的非线性依赖性。客户可能必须排队,直到他们回到到来为止,因此他们的订单决策相互作用。具体而言,在服务期间,客户知道队列长度并选择两个订单数量(或服务类型)之一。下一个补给(他们的活动时间)的时间是随机的,取决于订单数量。客户在服务期间和排队等待时不活跃。我们将预期活动与服务时间更大比率的服务类型称为“更有效”。在集中式的情况下,该系统有兴趣最大化稳态的活跃客户数量,这被称为系统的效率。我们表明,选择更有效的服务并不总是最佳的,但是可以通过选择取决于依赖非活动客户数量的三个阈值策略之一来很好地近似。在分散的情况下,每个客户都采取行动最大化她活跃的时间的比例。我们观察到个人和经理具有相反的激励措施:当队列长时间时,个人倾向于选择长期服务,而经理则在这种情况下更喜欢短暂的服务。这使系统难以调节。但是,我们表明,简单地删除效率较低的服务可以显着提高效率。
We study a make-to-order system with a finite set of customers. Production is stochastic with a nonlinear dependence between the ordered quantity and the production rate. Customers may have to queue until their turn arrives, and therefore their order decisions interact. Specifically, while being served, customers are aware of the queue length and choose one of two order quantities (or service types). The time to the next replenishment (their activity time) is stochastic and depends on the order quantities. A customer is inactive during service and while waiting in the queue. We refer to the type of service with a greater ratio of expected activity to service time as ``more efficient''. In the centralized case, the system is interested in maximizing the steady-state average number of active customers, which is referred to as the efficiency of the system. We show that choosing the more efficient service is not always optimal, but the optimal strategy can be approximated well by selecting one of three threshold strategies which depend on the number of inactive customers. In the decentralized case, each customer acts to maximize the fraction of time she is active. We observe that individuals and the manager have opposite incentives: When the queue is long, individuals tend to choose the long service, while the manager prefers the short service in this case. This makes the system difficult to regulate. However, we show that simply removing the less efficient service significantly increases efficiency.